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Shephard's Lemma
Shephard’s lemma is a major result in microeconomics having applications in
consumer choice and the theory of the firm.
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Shephard’s Lemma
Shephard’s lemma states that if indifference curves of the
expenditure or cost function are convex, then the cost minimizing
point of a given good (X) with price (PX) is unique. The idea is
that a consumer will buy a unique ideal amount of each item to
minimize the price for obtaining a certain level of utility given the
price of goods in the market. It was named after Ronald
Shephard who gave a proof using the distance formula in a paper
published in 1953, although it was already used by John Hicks
(1939) and Paul Samuelson (1947).
Sources: Wikipedia, http://dictionary.sensagent/shephard’s+lemma/en-en/
Shephard’s Lemma
Shephard’s lemma gives a precise formulation for the
demand for each good in the market with respect to that
level of utility and those prices: the derivative of the
expenditure function E(PX, PY, U) with respect to that price.
E
 X  hX (V ,PX ,PY )
PX